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is satis ed, the measurement is declared invalid and the corresponding measurement update (state and covariance) is skipped Repeated violations of the test condition can be used to declare the sensor invalid Use of such conditions to remove measurements deemed to be invalid can be problematic If the state error x = x x is for some reason larger than that predicted by P , then the above logic may remove all measurements In realistic applications, the conditions for discarding measurements is usually considerably more descriptive that indicated by eqn (581) In addition, when the condition r2 > (HP H + R) occurs, it is often useful to log an assortment of descriptive data (eg, yk , yk , x, Rk , Hk , and Hk P Hk ) The data logged at this condition may allow detection of k modeling errors or debugging of software errors

Question 1-1

birt pdf 417, birt ean 13, word aflame upc, word code 39, data matrix word 2010, birt code 128

points and vectors between rectangular coordinate systems Section 25 discusses plane rotations with derivations of speci c rotation matrices that are useful in navigation applications Since navigation systems are freely moving, one navigation system may rotate relative to another Therefore, Section 26 discusses the properties of time derivatives of vectors represented in and rotation matrices representing transformations between rotating reference frames Section 27 discusses methods to compute the direction cosine matrix based on measurements of the relative angular rate between two reference frames

Answer 1-1

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As previously motivated, navigation systems involve variables measured in various frames-of-reference To insure system interoperability and clear communication between engineers working with the system each frame and its properties should be clearly de ned As exempli ed in the introduction to this chapter, throughout this book, vectors and matrices will be written in boldface When a vector is represented relative to a speci c reference frame, the frame-of-reference will be indicated by a superscript For example, a is the vector represented with respect to the a frame-of-reference The rotation matrix for transforming a vector representation from frame a to frame b is written as Rb a where b = Rb a (21) a This equation is derived in Section 24 Speci c rotation matrices Rb will a be de ned in Section 25 Appendix A contains summary tables of the various coordinate frame, notation, variable, and constant de nitions used throughout this chapter and the remainder of the book Unless otherwise stated, all rectangular frames-of-reference are assumed to have three axes de ned to be orthonormal and right-handed Let the unit vectors along the coordinate axes of a reference frame be I, J, and K Orthonormality requires that I I=1 J I=0 K I=0 I J=0 J J=1 K J=0 I K=0 J K=0 K K=1

A number is an abstraction Numerals are tangible or physical symbols that represent numbers, such as 30 or 7 as they appear on this page A numeral is not a number, just as your name is not you

Question 1-2

where K I denotes the inner product between K and I Right-handed implies that I J = K Due to the gravitational e ects near the surface of the Earth, it is often convenient to consider ellipsoidal coordinate systems in addition to rectangular coordinate systems The Earth s geoid is a hypothetical equipotential surface of the Earth s gravitational eld that coincides with the Earth s

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In the Roman numeration system, how would we write the equivalents of the following decimal numerals (a) 10 (e) 100

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Answer 1-2

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